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(Hard.) Does the psychological environment affect the anatomy of the brain? This question was studied experimentally by Mark Rosenzweig and his associates. 20 The subjects for the study came from a genetically pure strain of rats. From each litter, one rat was selected at random for the treatment group, and one for the control group. Both groups got exactly the same kind of food and drink - as much as they wanted. But each animal in the treatment group lived with 11 others in a large cage, furnished with playthings which were changed daily. Animals in the control group lived in isolation, with no toys. After a month, the experimental animals were killed and dissected. On the average, the control animals were heavier and had heavier brains, perhaps because they ate more and got less exercise. However, " the itreatment group had consistently heavier cortexes (the "grey matter;" or thinking part of the brain). This experiment was repeated many times; results from the first 5 trials are shown in the table: "T" means treatment, and "C" is for control. Each line refers to one pair of animals. In the first pair, the animal in treatment had a cortex weighing 689 milligrams; the one in control had a lighter cortex, weighing only 657 milligrams. And so on. Two methods of analyzing the data will be presented in the form of exercises. Both methods take into account the pairing, which is a crucial feature of the data. (The pairing comes from randomization within litter.) (a) First analysis. How many paire there in all? In how many of these pairs did the treatment animal have a heavier cortex? Suppose treatment had no effect, so each animal of the pair had a \(50-50\) chance to have the heavier cortex, independently from pair to pair. Under this assumption, how likely is it that an investigator would get as many pairs as Rosenzweig did, or more, with the treatment animal having the heavier cortex? What do you infer? (b) Second analysis. For each pair of animals, compute the difference in cortex weights "treatment - control"." Find the average and SD of all these differences. The null hypothesis says that these differences are like draws made at random with replacement from a box whose average is \(0-\) the treatment has no effect. Make a z-test of this hypothesis. What do you infer? (c) To ensure the validity of the analysis, the following precaution was taken. "The brain dissection and analysis of each set of littermates was done in immediate succession but in a random order and identified only by code number so that the person doing the dissection does not know which cage the rat comes from." Comment briefly on the following: What was the point of this precaution? Was it a good idea?

Step by step solution

01

Count the Pairs

The study involved selecting one rat from each litter for both the treatment and control groups, hence each litter forms a pair. Count the total number of pairs from the given data to understand the sample size involved in the comparison of cortex weights.

02

Compare Cortex Weights Within Each Pair

For each pair, compare the cortex weight of the treatment rat to the control rat. Count how many times the cortex weight is heavier in the treatment group to check for patterns in the data.

03

Calculate Expected Outcomes Under Null Hypothesis

Under the null hypothesis, assume each rat in a pair has an equal 50% chance to have a heavier cortex purely by random selection. Calculate the probability of observing the number of pairs with heavier cortexes in the treatment group, as seen in the data or a greater number, using a binomial distribution.

04

Determine Hypothesis Inference from Probability

If the calculated probability is very low (commonly below 0.05), reject the null hypothesis. Conclude that the observed pairing outcome is unlikely due to chance, suggesting a psychological environmental influence on cortex weight.

05

Calculate Differences for Cortex Weights

For each pair, calculate the difference in cortex weight by subtracting the control weight from the treatment weight. This quantifies the difference in results within a pair.

06

Calculate Average and Standard Deviation of Differences

Compute the average and the standard deviation of these differences across all pairs to understand the central tendency and variability.

07

Perform the Z-Test

Using the average and standard deviation, perform a z-test to determine if the average difference significantly differs from zero. The null hypothesis assumes no effect, implying an average difference of zero.

08

Interpret Z-Test Results

If the z-test shows a significant deviation from zero, reject the null hypothesis, concluding that the treatment likely affects cortex weight. A nonsignificant result would fail to reject the null hypothesis.

09

Understand the Experimental Precaution

Randomizing the order of dissection and analyzing the coded brains ensures unbiased results by preventing researchers from knowing which group a rat belongs to during analysis. This removes potential bias from the results and strengthens validity.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Experimental Design

In psychological research, experimental design plays a crucial role in investigating the impact of various conditions on subject behavior or biology. In this specific study by Mark Rosenzweig and his team, the experimental design was set up to explore how living conditions affect rats' brain anatomy. By assigning rats randomly from each litter into a treatment or control group, the researchers ensured that any differences observed in brain anatomy could be attributed to environmental conditions rather than genetic variance.

• **Treatment Group:** Rats that lived together in a plaything-filled large cage.
• **Control Group:** Rats that lived in isolation, without toys.

Each rat was placed in these groups from the same genetic pool, enhancing the credibility of the results. The purpose of these groups was to compare how variations in psychological environment could potentially influence brain structure, particularly the cortex. This approach limits bias and lays a strong foundation for analyzing causal relationships.

Null Hypothesis Testing

Null hypothesis testing forms the backbone of statistical inference, providing a method to assess claims based on sample data. In this study, the null hypothesis posits that there is no effect of living conditions on brain cortex weight, meaning any observed differences are due to randomness.

To test this hypothesis, one assesses if the probability of observing the data, under the assumption that the null hypothesis is true, is sufficiently low to believe otherwise. If the probability or p-value falls below a critical threshold (commonly 0.05), the null hypothesis may be rejected. This suggests that differences in cortex weight are statistically significant, potentially linked to the psychological environment.
By formulating and testing the null hypothesis, researchers can determine if their findings support the idea of an environmental impact on brain anatomy.

Paired Comparison

A paired comparison is a method of comparing two related samples, in this case, pairs of rats from the same litter. This method allows for a more precise understanding of differences as it considers the inherent similarities due to genetic factors.

For each pair, the rat in the treatment group is directly compared with its littermate from the control group. By focusing on differences within these biologically similar pairs, researchers minimize the impact of individual variability and focus on the effect of the independent variable—in this case, the psychological environment.
Paired comparisons are especially potent in small sample sizes where variability is better accounted for, leading to more reliable comparisons.

Z-Test

A z-test is a statistical test used to determine if there is a significant difference between the means of two groups. In the context of the study, a z-test is applied to the differences in cortex weights between treatment and control pairs.

To perform a z-test, researchers calculate the mean and standard deviation of the differences in cortex weights. The test assesses whether the average of these differences significantly deviates from zero (as predicted by the null hypothesis).

• **If the z-score corresponds to a p-value below 0.05:** The results are significant, suggesting an environmental effect.
• **If not:** The null hypothesis stands, indicating a non-significant result.

This statistical tool helps researchers make inferences about the overall population based on sample data, offering a reliable method for hypothesis testing.

Binomial Distribution

The binomial distribution is a probability distribution that summarizes the likelihood that a value will take one of two independent states and applies them over multiple trials. In this study, it's used to assess the chance setup of observing a given number of pairs where the treatment group has a heavier cortex.

Assuming each rat has a 50% chance of being heavier by mere chance (null hypothesis), the binomial distribution helps calculate probabilities of winning outcomes (heavier brain) across observed pairs.
Using this distribution provides a mathematical framework for evaluating whether the number of observed heavier cortexes in the treatment group is due to chance or a real effect from the psychological environment.
In conclusion, binomial distribution is a powerful tool in determining the significance of outcomes in hypothesis testing.